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To obtain a driver’s license, you need to pass a written test and then pass a practical driving test.
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In May, 𝑛 people attempted to obtain a driver’s license from a particular branch of the Department of Motor Vehicles.
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90 percent of these people passed the written test.
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30 percent of those who passed the written test also passed the practical driving test.
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The number of people who passed both tests was 4050.
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What is the value of 𝑛?
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We’re told in the question that 𝑛 people attempted to obtain a driver’s license.
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90 percent of these people passed the written test.
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90 percent can be written as a decimal as 0.9.
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Therefore, 0.9𝑛 people passed the written test.
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30 percent of those who passed the written test also passed the practical test.
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As 30 percent is the same as 0.3, we could calculate the number of people who passed both tests by multiplying 0.3 by 0.9𝑛.
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Three multiplied by nine is equal to 27.
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Therefore, 0.3 multiplied by 0.9 is equal to 0.27.
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This means that an expression for the number of people who passed both tests is 0.27𝑛.
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We are also told in the question that this number is equal to 4050.
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We can therefore write the equation 0.27𝑛 is equal to 4050.
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To calculate the value of 𝑛, we can divide both sides by 0.27.
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On the left-hand side, we’re just left with 𝑛.
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4050 divided by 0.27 is equal to 15000.
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We can therefore say that the value of 𝑛, the number of people who attempted to obtain a driver’s license in May, is 15000.